Inhomogeneous media can change the nonlinear properties of waves propagating on them. In the ocean, this phenomenon can be observed when waves travel on a surface current. In the case of negative horizontal velocity gradients (i.e. an accelerating opposing current or a decelerating following current), waves shorten and heighten, enhancing wave steepness. As a result, a nonlinear mechanism known as modulational instability develops, leading to the formation of large-amplitude waves (the so-called rogue waves), even if they would otherwise be unexpected. Laboratory experiments and numerical simulations with a current-modified version of the Euler equations are presented to assess the role of an opposing current in changing the statistical properties of unidirectional random wave fields. Results demonstrate in a consistent and robust manner that an opposing current induces a sharp and rapid transition from weakly to strongly non-Gaussian properties with a consequent increase of the probability of occurrence of rogue waves. Agreement with numerical simulations confirms that this transformation can be attributed to quasi-resonant nonlinear interactions triggered by the background current.

Extreme waves larger than two times the significant wave height (also known as rogue waves) represent a serious threat for marine structures and operations (e.g. Clauss, 2002). Therefore, an accurate description of the statistical properties of the surface elevation and wave height can contribute to improving the design process and warning criteria for marine operations (Toffoli et al., 2005).

There are many mechanisms that cause large amplitude waves to occur (see Kharif and Pelinovsky, 2002; Onorato et al., 2013, for a complete review). Among them, nonlinear energy focusing due to the modulational instability of uniform wave trains to side band perturbations remains the most accredited (e.g. Janssen, 2004; Onorato et al., 2006; Toffoli et al., 2008; Onorato et al., 2009; Waseda et al., 2009; Babanin et al., 2011, Toffoli et al. 2013, among others). It has been verified theoretically and experimentally, however, that such mechanisms occur if waves are sufficiently steep and narrow banded both in the frequency and directional domain. Under these circumstances, rogue waves may occur within a fairly short scale of tens of wavelengths leading to substantial deviations from Gaussian and second-order-based statistics (e.g. Mori and Yasuda, 2002; Socquet-Juglard et al., 2005; Onorato et al., 2006; Onorato et al., 2009; Janssen, 2004; Toffoli et al. 2008; Waseda et al., 2009,; Toffoli et al., 2010; Toffoli et al. 2017 among others).